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Abstracts

Tasos Moulinos

Derived Azumaya Algebras and Twisted K-theory

Topological K-theory of dg-categories is a localizing invariant of dg-categories over
taking values in the -category of -modules. In this talk I describe a relative version
of this construction; namely for a quasi-compact, quasi-separated -scheme I construct a
functor valued in the -category of sheaves of spectra on , the complex points of . For inputs
of the form where is an Azumaya algebra over , I characterize the values
of this functor in terms of the twisted topological K-theory of . From this I deduce
a certain decomposition, for a finite CW-complex equipped with a bundle of projective
spaces over , of in terms of the twisted topological K-theory of ; this is
a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer
schemes.